Transcript Sequence analysis course

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Genome Analyis (Integrative
Bioinformatics & Genomics)
2008
Lecture 9
Pattern recognition
and phylogeny
Patterns
Some are easy some are
not
• Knitting patterns
• Cooking recipes
• Pictures (dot plots)
• Colour patterns
• Maps
In 2D and 3D humans are hard to be beat by a
computational pattern recognition technique,
but humans are not so consistent
Example of algorithm reuse:
Data clustering
• Many biological data analysis problems can
be formulated as clustering problems
– microarray gene expression data analysis
– identification of regulatory binding sites
(similarly, splice junction sites, translation start
sites, ......)
– (yeast) two-hybrid data analysis (experimental
technique for inference of protein complexes)
– phylogenetic tree clustering (for inference of
horizontally transferred genes)
– protein domain identification
– identification of structural motifs
– prediction reliability assessment of protein
structures
– NMR peak assignments
Data Clustering
Problems
• Clustering: partition a data set into clusters so that
data points of the same cluster are “similar” and
points of different clusters are “dissimilar”
• Cluster identification -- identifying clusters with
significantly different features than the background
Application Examples
• Regulatory binding site identification: CRP (CAP) binding
site
Gene expression data
• Two hybrid data analysisanalysis

These problems are all solvable by
a clustering algorithm
Multivariate statistics – Cluster
analysis
C1 C2 C3 C4 C5 C6 ..
1
2
3
4
5
Raw table
Any set of numbers per
column
•Multi-dimensional problems
•Objects can be viewed as a cloud
of points in a multidimensional
space
•Need ways to group the data
Multivariate statistics – Cluster
analysis
1
2
3
4
5
C1 C2 C3 C4 C5 C6 ..
Raw table
Any set of numbers per
column
Similarity criterion
Scores
5×5
Similarity
matrix
Cluster criterion
Dendrogram
Comparing sequences
- Similarity Score Many properties can be used:
• Nucleotide or amino acid composition
• Isoelectric point
• Molecular weight
• Morphological characters
• But: molecular evolution through sequence
alignment
Multivariate statistics – Cluster analysis
Now for sequences
1
2
3
4
5
Multiple sequence
alignment
Similarity criterion
Scores
5×5
Similarity
matrix
Cluster criterion
Phylogenetic tree
Lactate dehydrogenase multiple alignment
Human
Chicken
Dogfish
Lamprey
Barley
Maizey casei
Bacillus
Lacto__ste
Lacto_plant
Therma_mari
Bifido
Thermus_aqua
Mycoplasma
-KITVVGVGAVGMACAISILMKDLADELALVDVIEDKLKGEMMDLQHGSLFLRTPKIVSGKDYNVTANSKLVIITAGARQ
-KISVVGVGAVGMACAISILMKDLADELTLVDVVEDKLKGEMMDLQHGSLFLKTPKITSGKDYSVTAHSKLVIVTAGARQ
–KITVVGVGAVGMACAISILMKDLADEVALVDVMEDKLKGEMMDLQHGSLFLHTAKIVSGKDYSVSAGSKLVVITAGARQ
SKVTIVGVGQVGMAAAISVLLRDLADELALVDVVEDRLKGEMMDLLHGSLFLKTAKIVADKDYSVTAGSRLVVVTAGARQ
TKISVIGAGNVGMAIAQTILTQNLADEIALVDALPDKLRGEALDLQHAAAFLPRVRI-SGTDAAVTKNSDLVIVTAGARQ
-KVILVGDGAVGSSYAYAMVLQGIAQEIGIVDIFKDKTKGDAIDLSNALPFTSPKKIYSA-EYSDAKDADLVVITAGAPQ
TKVSVIGAGNVGMAIAQTILTRDLADEIALVDAVPDKLRGEMLDLQHAAAFLPRTRLVSGTDMSVTRGSDLVIVTAGARQ
-RVVVIGAGFVGASYVFALMNQGIADEIVLIDANESKAIGDAMDFNHGKVFAPKPVDIWHGDYDDCRDADLVVICAGANQ
QKVVLVGDGAVGSSYAFAMAQQGIAEEFVIVDVVKDRTKGDALDLEDAQAFTAPKKIYSG-EYSDCKDADLVVITAGAPQ
MKIGIVGLGRVGSSTAFALLMKGFAREMVLIDVDKKRAEGDALDLIHGTPFTRRANIYAG-DYADLKGSDVVIVAAGVPQ
-KLAVIGAGAVGSTLAFAAAQRGIAREIVLEDIAKERVEAEVLDMQHGSSFYPTVSIDGSDDPEICRDADMVVITAGPRQ
MKVGIVGSGFVGSATAYALVLQGVAREVVLVDLDRKLAQAHAEDILHATPFAHPVWVRSGW-YEDLEGARVVIVAAGVAQ
-KIALIGAGNVGNSFLYAAMNQGLASEYGIIDINPDFADGNAFDFEDASASLPFPISVSRYEYKDLKDADFIVITAGRPQ
Distance Matrix
1
2
3
4
5
6
7
8
9
10
11
12
13
Human
Chicken
Dogfish
Lamprey
Barley
Maizey
Lacto_casei
Bacillus_stea
Lacto_plant
Therma_mari
Bifido
Thermus_aqua
Mycoplasma
1
0.000
0.112
0.128
0.202
0.378
0.346
0.530
0.551
0.512
0.524
0.528
0.635
0.637
2
0.112
0.000
0.155
0.214
0.382
0.348
0.538
0.569
0.516
0.524
0.524
0.631
0.651
3
0.128
0.155
0.000
0.196
0.389
0.337
0.522
0.567
0.516
0.512
0.524
0.600
0.655
4
0.202
0.214
0.196
0.000
0.426
0.356
0.553
0.589
0.544
0.503
0.544
0.616
0.669
5
0.378
0.382
0.389
0.426
0.000
0.171
0.536
0.565
0.526
0.547
0.516
0.629
0.575
6
0.346
0.348
0.337
0.356
0.171
0.000
0.557
0.563
0.538
0.555
0.518
0.643
0.587
7
0.530
0.538
0.522
0.553
0.536
0.557
0.000
0.518
0.208
0.445
0.561
0.526
0.501
8
0.551
0.569
0.567
0.589
0.565
0.563
0.518
0.000
0.477
0.536
0.536
0.598
0.495
9
0.512
0.516
0.516
0.544
0.526
0.538
0.208
0.477
0.000
0.433
0.489
0.563
0.485
10
0.524
0.524
0.512
0.503
0.547
0.555
0.445
0.536
0.433
0.000
0.532
0.405
0.598
11
0.528
0.524
0.524
0.544
0.516
0.518
0.561
0.536
0.489
0.532
0.000
0.604
0.614
12
0.635
0.631
0.600
0.616
0.629
0.643
0.526
0.598
0.563
0.405
0.604
0.000
0.641
How can you see that this is a distance matrix?
13
0.637
0.651
0.655
0.669
0.575
0.587
0.501
0.495
0.485
0.598
0.614
0.641
0.000
Multivariate statistics – Cluster analysis
C1 C2 C3 C4 C5 C6 ..
1
2
3
4
5
Data table
Similarity criterion
Scores
Similarity
matrix
5×5
Cluster criterion
Dendrogram/tree
Multivariate statistics – Cluster
analysis
Why do it?
•
•
•
•
•
•
•
Finding a true typology
Model fitting
Prediction based on groups
Hypothesis testing
Data exploration
Data reduction
Hypothesis generation
But you can never prove a
classification/typology!
Cluster analysis – data normalisation/weighting
1
2
3
4
5
C1 C2 C3 C4 C5 C6 ..
Raw table
Normalisation criterion
1
2
3
4
5
C1 C2 C3 C4 C5 C6 ..
Normalised
table
Column normalisation
x/max
Column range normalise
(x-min)/(max-min)
Cluster analysis – (dis)similarity matrix
1
2
3
4
5
C1 C2 C3 C4 C5 C6 ..
Raw table
Similarity criterion
Scores
5×5
Similarity
matrix
Di,j = (k | xik – xjk|r)1/r Minkowski metrics
r = 2 Euclidean distance
r = 1 City block distance
(dis)similarity matrix
Di,j = (k | xik – xjk|r)1/r Minkowski metrics
r = 2 Euclidean distance
r = 1 City block distance
EXAMPLE:
length height width
Cow1
Cow 2
11
7
7
4
3
-2
3
4
5
Euclidean dist. = sqrt(42 + 32 + -22) = sqrt(29) = 5.39
City Block dist. = |4|+|3|+|-2| = 9
Cluster analysis – Clustering criteria
Scores
5×5
Similarity
matrix
Cluster criterion
Dendrogram (tree)
Single linkage - Nearest neighbour
Complete linkage – Furthest neighbour
Group averaging – UPGMA
Neighbour joining – global measure, used to make a
Phylogenetic Tree
Cluster analysis – Clustering criteria
Scores
5×5
Similarity
matrix
Cluster criterion
Dendrogram (tree)
Four different clustering criteria:
Single linkage - Nearest neighbour
Complete linkage – Furthest neighbour
Group averaging – UPGMA
Neighbour joining (global measure)
Note: these are all agglomerative cluster techniques; i.e. they proceed by
merging clusters as opposed to techniques that are divisive and proceed by
cutting clusters
Cluster analysis – Clustering criteria
1. Start with N clusters of 1 object each
2. Apply clustering distance criterion iteratively until
you have 1 cluster of N objects
3. Most interesting clustering somewhere in between
distance
Dendrogram (tree)
1 cluster
N clusters
Note: a dendrogram can be
rotated along branch points (like
mobile in baby room) -- distances
between objects are defined
along branches
Single linkage clustering (nearest
neighbour)
Char 2
Char 1
Single linkage clustering (nearest
neighbour)
Char 2
Char 1
Single linkage clustering (nearest
neighbour)
Char 2
Char 1
Single linkage clustering (nearest
neighbour)
Char 2
Char 1
Single linkage clustering (nearest
neighbour)
Char 2
Char 1
Single linkage clustering (nearest
neighbour)
Char 2
Char 1
Distance from point to cluster is defined as the
smallest distance between that point and any point in
the cluster
Single linkage clustering (nearest
neighbour)
Char 2
Char 1
Distance from point to cluster is defined as the
smallest distance between that point and any point in
the cluster
Single linkage clustering (nearest
neighbour)
Char 2
Char 1
Distance from point to cluster is defined as the
smallest distance between that point and any point in
the cluster
Single linkage clustering (nearest
neighbour)
Char 2
Char 1
Distance from point to cluster is defined as the
smallest distance between that point and any point in
the cluster
Single linkage clustering (nearest
neighbour)
Let Ci and Cj be two disjoint clusters:
di,j = Min(dp,q), where p  Ci and q  Cj
Single linkage dendrograms typically show
chaining behaviour (i.e., all the time a
single object is added to existing cluster)
Complete linkage clustering
(furthest neighbour)
Char 2
Char 1
Complete linkage clustering
(furthest neighbour)
Char 2
Char 1
Complete linkage clustering
(furthest neighbour)
Char 2
Char 1
Complete linkage clustering
(furthest neighbour)
Char 2
Char 1
Complete linkage clustering
(furthest neighbour)
Char 2
Char 1
Complete linkage clustering
(furthest neighbour)
Char 2
Char 1
Complete linkage clustering
(furthest neighbour)
Char 2
Char 1
Complete linkage clustering
(furthest neighbour)
Char 2
Char 1
Distance from point to cluster is defined as the
largest distance between that point and any point in
the cluster
Complete linkage clustering
(furthest neighbour)
Char 2
Char 1
Distance from point to cluster is defined as the
largest distance between that point and any point in
the cluster
Complete linkage clustering
(furthest neighbour)
Let Ci and Cj be two disjoint clusters:
di,j = Max(dp,q), where p  Ci and q  Cj
More ‘structured’ clusters than with
single linkage clustering
Clustering algorithm
1. Initialise (dis)similarity matrix
2. Take two points with smallest distance as
first cluster (later, points can be clusters)
3. Merge corresponding rows/columns in
(dis)similarity matrix
4. Repeat steps 2. and 3.
using appropriate cluster
measure when you need to calculate new
point-to-cluster or cluster-to-cluster
distances until last two clusters are
merged
Average linkage clustering
(Unweighted Pair Group Mean Averaging -UPGMA)
Char 2
Char 1
Distance from cluster to cluster is defined as the
average distance over all within-cluster distances
UPGMA
Let Ci and Cj be two disjoint clusters:
di,j =
1
————————
|Ci| × |Cj|
Ci
pq dp,q, where p  Ci and q  Cj
Cj
In words: calculate the average over all
pairwise inter-cluster distances
Multivariate statistics – Cluster analysis
1
2
3
4
5
C1 C2 C3 C4 C5 C6 ..
Data table
Similarity criterion
Scores
Similarity
matrix
5×5
Cluster criterion
Phylogenetic tree
Multivariate statistics – Cluster analysis
1
2
3
4
5
C1 C2 C3 C4 C5 C6
Similarity
criterion
Scores
6×6
Cluster criterion
Scores
5×5
Cluster criterion
Make two-way ordered
table using dendrograms
Multivariate statistics – Two-way cluster
analysis
C4 C3 C6 C1 C2 C5
1
4
2
5
3
Make two-way (rows, columns) ordered table using dendrograms;
This shows ‘blocks’ of numbers that are similar
Multivariate statistics – Two-way cluster analysis
Multivariate statistics – Principal
Component Analysis (PCA)
1
2
3
4
5
1
C1 C2 C3 C4 C5 C6
Similarity
Criterion:
Correlations
Correlations
6×6
2
Project data
points onto
new axes
(eigenvectors)
Calculate eigenvectors
with greatest
eigenvalues:
•Linear combinations
•Orthogonal
Multivariate statistics – Principal
Component Analysis (PCA)
Evolution/Phylogeny methods
Bioinformatics
“Nothing in Biology makes sense except
in the light of evolution” (Theodosius
Dobzhansky (1900-1975))
“Nothing in bioinformatics makes sense
except in the light of Biology”
Evolution
• Most of bioinformatics is comparative
biology
• Comparative biology is based upon
evolutionary relationships between
compared entities
• Evolutionary relationships are normally
depicted in a phylogenetic tree
Where can phylogeny be used
• For example, finding out about orthology
versus paralogy
• Predicting secondary structure of RNA
• Predicting protein-protein interaction
• Studying host-parasite relationships
• Mapping cell-bound receptors onto their
binding ligands
• Multiple sequence alignment (e.g. Clustal)
DNA evolution
• Gene nucleotide substitutions can be synonymous (i.e. not
changing the encoded amino acid) or nonsynonymous
(i.e. changing the a.a.).
• Rates of evolution vary tremendously among proteincoding genes. Molecular evolutionary studies have
revealed an ∼1000-fold range of nonsynonymous
substitution rates (Li and Graur 1991).
• The strength of negative (purifying) selection is thought
to be the most important factor in determining the rate of
evolution for the protein-coding regions of a gene
(Kimura 1983; Ohta 1992; Li 1997).
DNA evolution
• “Essential” and “nonessential” are classic molecular
genetic designations relating to organismal fitness.
– A gene is considered to be essential if a knock-out results in
(conditional) lethality or infertility.
– Nonessential genes are those for which knock-outs yield viable
and fertile individuals.
• Given the role of purifying selection in determining
evolutionary rates, the greater levels of purifying
selection on essential genes leads to a lower rate of
evolution relative to that of nonessential genes
• This leads to the observation: “What is important is
conserved”.
Reminder -- Orthology/paralogy
Orthologous genes are homologous
(corresponding) genes in different
species
Paralogous genes are homologous genes
within the same species (genome)
Old Dogma – Recapitulation Theory
(1866)
Ernst Haeckel:
“Ontogeny recapitulates
phylogeny”
•
•
Ontogeny is the development of the
embryo of a given species;
phylogeny is the evolutionary
history of a species
http://en.wikipedia.org/wiki/Recapitulation_theory
Haeckels drawing in support of his
theory: For example, the human
embryo with gill slits in the neck was
believed by Haeckel to not only signify
a fishlike ancestor, but it represented a
total fishlike stage in development.
However,gill slits are not the same as
gills and are not functional.
Phylogenetic tree (unrooted)
Drosophila
human
internal node
fugu
mouse
leaf
edge
OTU –
Observed
taxonomic unit
Phylogenetic tree (unrooted)
Drosophila
root
human
internal node
fugu
mouse
leaf
edge
OTU –
Observed
taxonomic unit
Phylogenetic tree (rooted)
root
time
edge
internal node (ancestor)
leaf
OTU – Observed
taxonomic unit
How to root a tree
• Outgroup – place root between
distant sequence and rest group
• Midpoint – place root at
midpoint of longest path (sum of
branches between any two
OTUs)
f
m
D
h
f
m
1
f
4
h
2
3
1
5
m
1
2
1
h
D
f
m
1
h
D
f-
• Gene duplication – place root
between paralogous gene copies
3
D
h-
f-
h-
f- h- f- h-
Combinatoric explosion
Number of unrooted trees
Number of rooted trees
=
=
2n  5!
n 3
2 n  3!
2n  3!
n2
2 n  2!
Combinatoric explosion
# sequences
2
3
4
5
6
7
8
9
10
# unrooted
trees
1
1
3
15
105
945
10,395
135,135
2,027,025
# rooted
trees
1
3
15
105
945
10,395
135,135
2,027,025
34,459,425
Tree distances
Evolutionary (sequence distance) = sequence dissimilarity
human
5
x
human
1
mouse
6
x
fugu
7
3
x
Drosophila
14
10
9
mouse
2
1
1
x
fugu
6
Drosophila
Note that with evolutionary methods for generating trees you get distances
between objects by walking from one to the other.
Phylogeny methods
1. Distance based – pairwise distances (input is
distance matrix)
2. Parsimony – fewest number of evolutionary events
(mutations) – relatively often fails to reconstruct
correct phylogeny, but methods have improved
recently
3. Maximum likelihood – L = Pr[Data|Tree] – most
flexible class of methods - user-specified
evolutionary methods can be used
Similarity criterion for phylogeny
• A number of methods (e.g. ClustalW) use sequence
identity with Kimura (1983) correction:
Corrected K = - ln(1.0-K-K2/5.0), where K is percentage
divergence (expressed as sequence identity difference)
corresponding to two aligned sequences (often only taking
the gap-less alignment columns into account)
• There are various models to correct for the fact that
the true rate of evolution cannot be observed through
nucleotide (or amino acid) exchange patterns (e.g.
back mutations)
• Saturation level is ~94% changed sequences, higher
real mutations are no longer observable
Distance based --UPGMA
Let Ci and Cj be two disjoint clusters:
1
di,j = ———————— pq dp,q, where p  Ci and q  Cj
|Ci| × |Cj|
Ci
Cj
In words: calculate the average over all pairwise
inter-cluster distances
Clustering algorithm: UPGMA
Initialisation:
•
Fill distance matrix with pairwise distances
•
Start with N clusters of 1 element each
Iteration:
1. Merge cluster Ci and Cj for which dij is minimal
2. Place internal node connecting Ci and Cj at height dij/2
3. Delete Ci and Cj (keep internal node)
Termination:
•
When two clusters i, j remain, place root of tree at height dij/2
d
Ultrametric Distances
•A tree T in a metric space (M,d) where d is ultrametric
has the following property: there is a way to place a root
on T so that for all nodes in M, their distance to the root
is the same. Such T is referred to as a uniform
molecular clock tree.
•(M,d) is ultrametric if for every set of three elements
i,j,k∈M, two of the distances coincide and are greater
than or equal to the third one (see next slide).
•UPGMA is guaranteed to build correct
tree if distances are ultrametric. But it fails
if not!
Ultrametric Distances
Given three leaves, two distances are equal
while a third is smaller:
d(i,j)  d(i,k) = d(j,k)
a+a  a+b = a+b
i
a
b
a
j
k
nodes i and j are at same
evolutionary distance from k
– dendrogram will therefore
have ‘aligned’ leafs; i.e. they
are all at same distance
from root
No need to memorise formula
Evolutionary clock speeds
Uniform clock: Ultrametric
distances lead to identical
distances from root to leafs
Non-uniform evolutionary clock: leaves have different
distances to the root -- an important property is that of
additive trees. These are trees where the distance between
any pair of leaves is the sum of the lengths of edges
connecting them. Such trees obey the so-called 4-point
condition (next slide).
Additive trees
All distances satisfy 4-point condition:
For all leaves i,j,k,l:
d(i,j) + d(k,l)  d(i,k)
+ d(j,l)
=
d(i,l) + d(j,k)
(a+b)+(c+d)  (a+m+c)+(b+m+d) = (a+m+d)+(b+m+c)
k
i
a
c
m
j
b
d
l
Result: all pairwise distances obtained by traversing
No need to memorise formula
the tree
Additive trees
In additive trees, the distance between any pair
of leaves is the sum of lengths of edges
connecting them
Given a set of additive distances: a unique tree T
can be constructed:
•For two neighbouring leaves i,j with common
parent k, place parent node k at a distance
from any node m with
d(k,m) = ½ (d(i,m) + d(j,m) – d(i,j))
i
c
= ½ ((a+c) + (b+c) – (a+b))
No need to memorise formula
a
b
j
c
k
m
Utrametric/Additive distances
If d is ultrametric then d is additive
If d is additive it does not follow that d is
ultrametric
Can you prove the first statement?
Distance based -Neighbour
joining (Saitou and Nei, 1987)
• Widely used method to cluster DNA
or protein sequences
• Global measure – keeps total branch
length minimal, tends to produce a
tree with minimal total branch length
(concept of minimal evolution)
• Agglomerative algorithm
• Leads to unrooted tree
Neighbour-Joining (Cont.)
• Guaranteed to produce correct tree if
distances are additive
• May even produce good tree if
distances are not additive
• At each step, join two nodes such
that total tree distances are minimal
(whereby the number of nodes is
decreased by 1)
Neighbour-Joining
• Contrary to UPGMA, NJ does not assume taxa to be
equidistant from the root
• NJ corrects for unequal evolutionary rates between
sequences by using a conversion step
• This conversion step requires the calculation of
converted (corrected) distances, r-values (ri) and
transformed r values (r’i), where ri = dij and r’i = ri /(n2), with n each time the number of (remaining) nodes in
the tree
• Procedure:
– NJ begins with an unresolved star tree by joining all taxa onto
a single node
– Progressively, the tree is decomposed (star decomposition),
by selecting each time the taxa with the shortest corrected
distance, until all internal nodes are resolved
Neighbour joining
x
y
y
y
x
(a)
x y
(d)
(c)
(b)
z
y
x
(e)
(f)
At each step all possible ‘neighbour joinings’ are checked and the one
corresponding to the minimal total tree length (calculated by adding all
branch lengths) is taken.
Neighbour joining – ‘correcting’
distances
Finding neighbouring leaves:
Define
d’ij = dij – ½ (ri + rj)
[d’ij is corrected distance]
Where
ri = k dik and
1
r’i =
——— k dik
|L| - 2
[ |L| is current number of nodes]
Total tree length Dij is minimal iff i and j are
neighbours
No need to memorise
Algorithm: Neighbour joining
Initialisation:
•Define T to be set of leaf nodes, one per sequence
•Let L = T
Iteration:
•Pick i,j (neighbours) such that d’i,j is minimal (minimal total tree
length) [this does not mean that the OTU-pair with smallest
uncorrected distance is selected!]
•Define new ancestral node k, and set dkm = ½ (dim + djm – dij) for
all m  L
•Add k to T, with edges of length dik = ½ (dij + r’i – r’j)
•Remove i,j from L; Add k to L
Termination:
•When L consists of two nodes i,j and the edge between them of
length dij
No need to memorise, but know how NJ works intuitively
Algorithm: Neighbour joining
NJ algorithm in words:
1. Make star tree with ‘fake’ distances (we need these to be
able to calculate total branch length)
2. Check all n(n-1)/2 possible pairs and join the pair that leads
to smallest total branch length. You do this for each pair by
calculating the real branch lengths from the pair to the
common ancestor node (which is created here – ‘y’ in the
preceding slide) and from the latter node to the tree
3. Select the pair that leads to the smallest total branch length
(by adding up real and ‘fake’ distances). Record and then
delete the pair and their two branches to the ancestral node,
but keep the new ancestral node. The tree is now 1 one node
smaller than before.
4. Go to 2, unless you are done and have a complete tree with
all real branch lengths (recorded in preceding step)
Parsimony & Distance
Sequences
Drosophila
fugu
mouse
human
1
t
a
a
a
2
t
a
a
a
3
a
t
a
a
4
t
t
a
a
5
t
t
a
a
6
a
a
t
a
human
x
mouse
2
x
fugu
4
4
x
Drosophila
5
5
3
7
a
a
a
t
parsimony
Drosophila
1
4
2
fugu
Drosophila
5
3
mouse
6
7
human
distance
mouse
2
1
2
1
x
fugu
1
human
Problem: Long Branch Attraction
(LBA)
• Particular problem associated with parsimony
methods
• Rapidly evolving taxa are placed together in a tree
regardless of their true position
• Partly due to assumption in parsimony that all
lineages evolve at the same rate
• This means that also UPGMA suffers from LBA
• Some evidence exists that also implicates NJ
A
A
B
C
True tree
D
B
C
D
Inferred tree
Maximum likelihood
Pioneered by Joe Felsenstein
• If data=alignment, hypothesis = tree, and under a given
evolutionary model,
maximum likelihood selects the hypothesis (tree) that
maximises the observed data
• A statistical (Bayesian) way of looking at this is that the tree
with the largest posterior probability is calculated based on the
prior probabilities; i.e. the evolutionary model (or
observations).
• Extremely time consuming method
• We also can test the relative fit to the tree of different models
(Huelsenbeck & Rannala, 1997)
Maximum likelihood
Methods to calculate ML tree:
• Phylip (http://evolution.genetics.washington.edu/phylip.html)
• Paup (http://paup.csit.fsu.edu/index.html)
• MrBayes (http://mrbayes.csit.fsu.edu/index.php)
Method to analyse phylogenetic tree with ML:
• PAML (http://abacus.gene.ucl.ac.uk/software/paml.htm)
The strength of PAML is its collection of sophisticated substitution models to
analyse trees.
• Programs such as PAML can test the relative fit to the
tree of different models (Huelsenbeck & Rannala, 1997)
Maximum likelihood
• A number of ML tree packages (e.g. Phylip, PAML)
contain tree algorithms that include the assumption of a
uniform molecular clock as well as algorithms that don’t
• These can both be run on a given tree, after which the
results can be used to estimate the probability of a
uniform clock.
How to assess confidence in tree
How to assess confidence in tree
• Distance method – bootstrap:
– Select multiple alignment columns with
replacement (scramble the MSA)
– Recalculate tree
– Compare branches with original (target) tree
– Repeat 100-1000 times, so calculate 1001000 different trees
– How often is branching (point between 3
nodes) preserved for each internal node in
these 100-1000 trees?
– Bootstrapping uses resampling of the data
The Bootstrap -- example
Original
1
M
M
2
C
A
C
3
V
V
L
4
K
R
R
5
V
L
2x
3
V
Scrambled V
L
4
K
R
R
3
V
V
L
6
I
I
L
7
Y
F
F
8
S
S
T
8
S
S
T
6
I
I
L
Used multiple times in
resampled (scrambled)
MSA below
5
1
2
3
4
3x
8
S
S
T
6
I
I
L
6
I
I
L
Only boxed alignment columns are randomly selected in this example
1
1
2
5
3
Nonsupportive
Some versatile phylogeny software
packages
• MrBayes
• Paup
• Phylip
MrBayes: Bayesian Inference of
Phylogeny
• MrBayes is a program for the Bayesian estimation of phylogeny.
• Bayesian inference of phylogeny is based upon a quantity called the
posterior probability distribution of trees, which is the probability of
a tree conditioned on the observations.
• The conditioning is accomplished using Bayes's theorem. The
posterior probability distribution of trees is impossible to calculate
analytically; instead, MrBayes uses a simulation technique called
Markov chain Monte Carlo (or MCMC) to approximate the posterior
probabilities of trees.
• The program takes as input a character matrix in a NEXUS file
format. The output is several files with the parameters that were
sampled by the MCMC algorithm. MrBayes can summarize the
information in these files for the user.
No need to memorise
MrBayes: Bayesian Inference of
Phylogeny
MrBayes program features include:
• A common command-line interface for Macintosh, Windows, and UNIX
operating systems;
• Extensive help available via the command line;
• Ability to analyze nucleotide, amino acid, restriction site, and morphological
data;
• Mixing of data types, such as molecular and morphological characters, in a
single analysis;
• A general method for assigning parameters across data partitions;
• An abundance of evolutionary models, including 4 X 4, doublet, and codon
models for nucleotide data and many of the standard rate matrices for amino
acid data;
• Estimation of positively selected sites in a fully hierarchical Bayes framework;
• The ability to spread jobs over a cluster of computers using MPI (for Macintosh
and UNIX environments only).
No need to memorise
PAUP
Phylip – by Joe Felsenstein
Phylip programs by type of data
• DNA sequences
• Protein sequences
• Restriction sites
• Distance matrices
• Gene frequencies
• Quantitative characters
• Discrete characters
• tree plotting, consensus trees, tree distances and tree
manipulation
http://evolution.genetics.washington.edu/phylip.html
Phylip – by Joe Felsenstein
Phylip programs by type of algorithm
• Heuristic tree search
• Branch-and-bound tree search
• Interactive tree manipulation
• Plotting trees, consenus trees, tree distances
• Converting data, making distances or bootstrap
replicates
http://evolution.genetics.washington.edu/phylip.html
The Newick tree format
C
A
Ancestor1
5
3
4
E
D
B
6
5
11
(B,(A,C,E),D); -- tree topology
root
(B:6.0,(A:5.0,C:3.0,E:4.0):5.0,D:11.0); -- with branch lengths
(B:6.0,(A:5.0,C:3.0,E:4.0)Ancestor1:5.0,D:11.0)Root;
-- with branch lengths and ancestral node names
Distance methods: fastest
• Clustering criterion using a distance matrix
• Distance matrix filled with alignment scores
(sequence identity, alignment scores, Evalues, etc.)
• Cluster criterion
Kimura’s correction for protein
sequences (1983)
This method is used for proteins only. Gaps are ignored and only
exact matches and mismatches contribute to the match score.
Distances get ‘stretched’ to correct for back mutations
S = m/npos,
Where m is the number of exact matches and
npos the number of positions scored
D = 1-S
Corrected distance = -ln(1 - D - 0.2D2)
(see also
earlier slide)
Reference:
M. Kimura, The Neutral Theory of Molecular Evolution, Camb.
Uni. Press, Camb., 1983.
Sequence similarity criteria for
phylogeny
• In
addition to the Kimura correction, there are
various models to correct for the fact that the true
rate of evolution cannot be observed through
nucleotide (or amino acid) exchange patterns (e.g.
due to back mutations).
• Saturation level is ~94%, higher real mutations
are no longer observable
A widely used protocol to infer
a phylogenetic tree
• Make an MSA
• Take only gapless positions and
calculate pairwise sequence distances
using Kimura correction
• Fill distance matrix with corrected
distances
• Calculate a phylogenetic tree using
Neigbour Joining (NJ)
Phylogeny disclaimer
• With all of the phylogenetic methods,
you calculate one tree out of very many
alternatives.
• Only one tree can be correct and depict
evolution accurately.
• Incorrect trees will often lead to ‘more
interesting’ phylogenies, e.g. the whale
originated from the fruit fly etc.
Take home messages
• Rooted/unrooted trees, how to root a tree
• Make sure you can do the UPGMA algorithm
and understand the basic steps of the NJ
algorithm
• Understand the three basic classes of
phylogenetic methods: distance-based,
parsimony and maximum likelihood
• Make sure you understand bootstrapping (to
asses confidence in tree splits)